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Reflection on Math Art Project

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When we were first deciding on which art piece to choose we had everyone pick 2 of their favourites and we would pick one that everyone agreed on. Our decision led us to the piece by Margaret Kepner. Her spiral contained 400+ numbers and I didn't know how to recreate it without drawing it by hand. Fortunately, Kyle was able to write a code in LaTeX that made life much easier. Original At first, I thought the concept(prime numbers) behind the art was a little too simple. But there was much more to understand, such as the different types of numbers (happy, triangular, lucky, etc.). Also the Ulam Spiral, which was the inspiration for her piece, was very interesting to learn about. It was more complex than I expected! Replica When we were to put our own spin on the spiral, we had to think of 3 different types of numbers we could use instead of prime/happy/triangular numbers. We did some research on different types of numbers and ended up with going with prime/lucky/perfect...
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The Dishes Problem

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"How many guests are there?" said the official. "I don't know.", said the cook, "but every 2 used a dish of rice, every 3 used a dish of broth, and every 4 used a dish of meat between them".  There were 65 dishes in all.  How many guests were there? The first thing I thought of was lowest common multiples(LCM). So the LCM between 2,3, and 4 is 12. That means if we had a group of 12 people, there would be a set number of dishes. So if we had 12 people, there would need to be 6 rice dishes, 4 broth, and 3 meat. 12 People => 6 Rice + 4 Broth + 3 Meat = 13 Dishes So for 12 people we have 13 dishes in total. Now we just think how many groups of 13 dishes are in 65 dishes, which is 5 groups. So we need to count 5 groups of 12 people, which is 60 people. I think it's interesting to pose these puzzles from different cultures because it's neat to see how different cultures utilize math. But despite these different cultures, the basis of math...
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Instrumental vs. Relational

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Richard Skemp describes instrumental understanding as 'rules without reason'. When he was giving such examples in math, it made me think of my time as a student in high school. I remember learning trigonometric identities and using them to solve problems, but I didn't understand what  they truly meant. I did not understand where  they came from and why   we used them, I only understood how  to apply them. This is the main difference between what Skemp describes as relational vs. instrumental understanding. Relational understanding answers why,  whereas instrumental only answers  how . Skemp tells us of these mathematical mis-matches, where the student's goal is to understand instrumentally, while being taught by a teacher wants them to understand relationally. Up until grade 10, I was one of these students who only had a instrumental understanding of mathematics. I had an amazing teacher who taught us in this relational way of understanding. This teacher ...
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